Geometry Formulas: Surface Area & Volume

A formula is just a set of instructions. It tells you exactly what to do! All you have to do is look at the picture and identify the parts. Substitute numbers for the variables and do the math. That’s it!

Let’s start in the beginning… Before you can do surface area or volume, you have to know the following formulas. RectangleA = lw TriangleA = ½ bh CircleA = π r² C = πd

You can tell the base and height of a triangle by finding the right angle: TRIANGLES

CIRCLES You must know the difference between RADIUS and DIAMETER. r d

Let’s start with a rectangular prism. Surface area can be done using the formula SA = 2 lw + 2 wl + 2 lw OR Either method will gve you the same answer. you can find the area for each surface and add them up. Volume of a rectangular prism is V = lwh

Example: 7 cm 4 cm 8 cm Front/back 2(8)(4) = 64 Left/right 2(4)(7) = 56 Top/bottom 2(8)(7) = 112 Add them up! SA = 232 cm² V = lwh V = 8(4)(7) V = 224 cm³

To find the surface area of a triangular prism you need to be able to imagine that you can take the prism apart like so: Notice there are TWO congruent triangles and THREE rectangles. The rectangles may or may not all be the same. Find each area, then add.

Example: 8mm 9mm 6 mm 6mm Find the AREA of each SURFACE 1. Top or bottom triangle: A = ½ bh A = ½ (6)(6) A = The two dark sides are the same. A = lw A = 6(9) A = The back rectangle is different A = lw A = 8(9) A = 72 ADD THEM ALL UP! SA = 216 mm²

Volume of Prisms or Cylinders You already know how to find the volume of a rectangular prism: V = lwh The new formulas you need are: Triangular Prism V = ( ½ bh )(H) h = the height of the triangle and H = the height of the cylinder Cylinder V = (πr²)(H)

Volume of a Triangular Prism We used this drawing for our surface area example. Now we will find the volume. V = ( ½ bh )(H) V = ½(6)(6)(9) V = 162 mm³ This is a right triangle, so the sides are also the base and height. Height of the prism

Try one: Can you see the triangular bases? V = ( ½ bh )(H) V = ( ½)(12)(8)(18) V = 864 cm³ Notice the prism is on its side. 18 cm is the HEIGHT of the prism. Picture if you turned it upward and you can see why it’s called “height”.

V = (πr²)(H) V = (π)(3.1²)(12) V = (π)(3.1)(3.1)(12) V = in³ Volume of a Cylinder We used this drawing for our surface area example. Now we will find the volume. optional step!

Try one: 10 m d = 8 m V = (πr²)(H) V = (π)(4²)(10) V = (π)(16)(10) V = m³ Since d = 8, then r = 4 r² = 4² = 4(4) = 16

Here are the formulas you will need to know: A = lwSA = 2πrh + 2πr² A = ½ bh V = ( ½ bh )(H) A = π r²V = (πr²)(H) C = πd and how to find the surface area of a prism by adding up the areas of all the surfaces